EconS 301, Spring 2015, Dr. Rosenman Test 1

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1 EconS 301, Spring 2015, Dr. Rosenman Test 1 Do any three of questions 1, 2, 3 and 4, and do question 5. The three questions you do out of 1-4 are worth 10 points each, and question 5 is worth 20 points. I am figuring 10 minutes each for the first 3, and 30 minutes for question 5. That leaves 15 minutes for panic and other activities. 1. Consider the following demand and supply for bicycles: Qd=600-3P-5T+5M and Qs=-100+P where P is the price of bicycles, T is the price of tires and M is income in 1000s of dollars. a. If T=10 and M=30, find the equilibrium price of bicycles. b. At the equilibrium values, calculate the price elasticity of demand and the price elasticity of supply. c. At the equilibrium values, calculate the cross price elasticity of demand for bicycles with respect to the price of tires, and indicate if they are substitutes or complements. d. At the equilibrium values, calculate the income elasticity of demand for bicycles and what type of good we would classify bicycles as. a. Qd=600-3P-5T+5M=600-3P =700-3P Q=-100+P so Qd=Qs 700-3P=-100+P 800=4P or 200=Pe. Using this in either the D or S curve gives Qe=100. b. e p=(dqd/dp)*(p/qd). From the demand curve (dqd/dp)=-3. So e p=-3*(200/100)=-6. e s=(dqs/dp)*(p/qs). From the supply curve (dqs/dp)=1. So e s=1*(200/100)=2. c. e x=(dqd/dpt)*(pt/qd). From the demand curve (dqd/dpt)=-5. So e p=-5*(10/100)=-0.5 which indicates they are complements. d. e M=(dQd/dM)*(M/Qd). From the demand curve (dqd/dpt)=5. So e M=5*(30/100)=1.5 which indicates bicycles are a luxury good.

2 2. Ann has a utility function U(x,y)=x 2 y a. Find Ann s demand curve for x as a function of P x, P y and income (I). b. Find her income elasticity of demand for x and her cross-price elasticity of demand for x with respect to the price of y. c. If x costs $8 per unit and y cost $2 per unit and income is $240 find Ann s utility maximizing choice of x and y. d. What is the marginal rate of substitution of x for y when utility is maximized? e. If the price of x decreases to $6 per unit, will Ann s marginal rate of substitution of x for y increase or decrease? Explain if her consumption of X will increase or decrease, and how. a. Form the lagarngian, L=X 2 Y-λ(M-PxX-PyY) L/ x=2xy+λpx=0 and L/ yx=x 2 +λpy=0 (2Y)/X = Px/Py sp 2YPy=PxX or PyY=PxX/2 L/ λ=m-pxx-pyy=0 M=PxX+PxX/2 M=1.5PxX or X=M/(1.5Px) b. e M=(dX/dM) (M/X)=(1/1.5) (M/X) and. e Py=(dX/dM) (Py/X)=0 (M/X)=0 c. From part a, X=M/(1.5)Px)=240/(1.5 8)=240/12=20 Notice PxX=160 We know PyY=PxX/2=160/2=80 so Y=40 d. MRS=Mux/MUy=2XY/X 2 =2Y/X=80/20=4 e. For utility max we need MRS=Px/Py. If Px/Py changes to 6/2=3 Ann needs to lower her MRS. She does that by MUx and MUy which is accomplished by X and/or Y.

3 3. In March 2005, President Bush imposed tariffs of 8-30% on imported steel to protect the US steel industry. Most steel is used by other firms, so the demand for steel comes from companies that make automobiles or do major construction projects. Their quantity demanded for steel is a good indicator of how much they produce. Suppose these companies use steel from both US steel producers and foreign producers a. Graphically, show how the tariffs affected equilibrium price and quantity of steel bought by domestic automobile and construction firms. Explain what your graph shows. b. Explain, using your graph how it changed the producer s surplus of both domestic and foreign steel producers. c. Indicate how much revenue the government collected from the tariff. d. Critics of the tariff argued that it cost more jobs than it created. Referring to your graph, explain what they meant. P2 P1..P2-T g Sf+T Sf d P2 P1 f e a b c Sd P2 P1 D S+T S Qf2 Qf1 Qd1 Qd2 Q2 Q1 Foreign Domestic Total a. The amount bought by automobile and construction decreases from Q1 to Q2. The amount supplied domestically increases from Qd1 to Qd2. The amount supplied from foreign sources decreases from Qf1 to Qf2. b. Foreign producer surplus falls from triangle gfp1 to triangle formed by the line P2g and the heavy dotted supply curve Sf+T. Domestic producer surplus increases from abp1 to acp2 c. Government will collect rectangle (P2-T)edP2=T Qf2 d. They are arguing that the jobs created in the steel industry (implied by the increase from Qd1 to Qd2 are fewer than the lost jobs in the automobile and construction industries by the decrease in steel bought from Q1 to Q2.

4 4. The Affordable Care Act forces people to buy health insurance if they don t get coverage through work. To make the problem easier, assume people already buy some health insurance, but the ACA makes them buy more. a. Using an indifference curve analysis, show that for many people the ACA lowers their utility. b. For low income people there is a tax credit which rebates part of the cost of buying the health insurance. Suppose the tax credit is equal to their cost of buying the required insurance. Show that their utility be higher than without the ACA, but potentially lower than if they were just given an equal sized cash grant. c. One possible different policy is to offer a subsidy on the price of health insurance. A critique of this policy is that it will not increase health insurance as much, even if the total subsidy is the same. Decompose the price decrease into income and substitution effects, and show that if the amount of health insurance bought is less than the equivalent cost of a health insurance tax credit, it must mean that other goods are normal goods. Other goods 5 U1 1 3 U3 4 2 U2 H1 H2 Health Insurance a. Without the ACA, people consume at point 1 with H1 health insurance. If they are forced to buy H2, there utility falls to U2 b. The full credit means they are given H2-H1 health insurance for free, shifting the budget constraint out to the dotted line. Since it is parallel, it is like a cash grant of equal value. Clearly utility increases to U3 with consumption at 3, but unless health insurance has no income effect (unlikely) it will not be utility maximizing. c. A price subsidy for health insurance moves the budget constraint to the light dotted line. To be equal cost, it must go through point 3. Optimum with this budget constraint is point 5 (where the arrow points). The substitution effect is from point 3 to point 5. The income effect is from point 5 to point 4. Since 4 is to the left of point 1, that implies the income effect for other goods is positive.

5 5. For any FIVE (5) of the statements below, indicate if it is True, False or Uncertain, and explain why. Each is worth 4 points. You may also choose TWO (2) additional questions as extra credit on the test. Each extra credit question is worth 2.5 points. Clearly indicate which questions are for extra credit. If you don t, the first 5 you do will be the regular test questions. a. Tim consumes only goods A and B. Good B is a normal good. The local government has a referendum allowing people to choose among two taxes. The first tax will apply only to good B. The second tax will apply to both goods equally. The two taxes raise the same revenue. Tim will vote for the second tax. True. The equivalent variation shows that a tax on one good introduces extra distortion (the substitution effect) that lowers utility more than if all goods are taxes at the same rate. b. Flatter indifference curves have larger income effects. Uncertain. The flatness of the indifference curve says nothing about the income effect. It can be large or small. c. The price of food increases by 10% and you spend a larger fraction of your income on it. The good is a luxury good. Uncertain. A luxury good is defined by being very responsive to income. The information tells us about the price elasticity, but nothing about the income elasticity. d. The price of food decreases by 10%. After the price change you spend a larger fraction of your income on other goods. For you the price elasticity of demand for food is inelastic. True. If you are spending a larger fraction of your income on other goods, which means you are spending a smaller fraction of your income on Food. This implies the % P>% F so the price elasticity of demand for food is inelastic. More simply, since income hasn t changed, if you are spending more on other goods, you are spending less on Food. Since price fell, that means it is inelastic e. Due to a flood, corn prices and soybean prices both increase. If corn and soybeans are substitutes the equilibrium quantity of corn demanded falls. The flood shifts the supply curve for both soybeans and corn in, but the increase in the price of soybean shifts the demand for corn out. Hence, we are sure the price of corn goes up, but the change in the equilibrium quantity is uncertain. f. If pizza and calzones are substitutes, the income effect of a price increase for pizza must show that pizza is an inferior good. Uncertain. The increase in price will but have a substitution effect towards calzones, but says nothing about the income effect. g. For Mitzi shampoo and conditioner are perfect complements. For each squirt of shampoo she uses one squirt of conditioner. Mitzi s indifference curve for shampoo and conditioner is a straight line with a slope of -1. False. She will have a fixed proportion (L-shaped) indifference curves.

6 h. China recently relaxed its rules against the import of apples from Washington State. Previously, there was a quota on Washington apple imports to China. Washington apple producers would have preferred the Chinese impose a tariff (tax) on their apples instead of the quota, even if it resulted in the same amount of exports from Washington to China. False. For equal sized imports, a quota affect producer surplus less for the exporting country than does a tariff i. An increase in gas taxes rebated to consumers through an income tax credit will likely decrease the use of gasoline, and leave consumers equally well off in terms of utility as if there was no tax. False. It introduces a distortion. By revealed preference (or a graph) they have the same income, but because the price of gas in higher, they can no longer afford their old consumption point, so utility must be lower. j. The supply of health insurance is relatively steep, while the demand for health insurance is relatively flat. The subsidy provided by the ACA increases seller s surplus more than it increases consumer surplus. As the graph shows, the seller s surplus goes up much more that does the consumers surplus. k. If the slope of a price-consumption line is horizontal when price of the good on the horizontal axis is changing, the income effect must be zero. If the price-consumption line is horizontal, the amount spent on other goods is not changing. The substitution effect indicates the amount of the good consumed goes down, so the amount spent on the good would go down. The horizontal price-consumption line also indicates the amount spend on the good with the price increase would go down. But that doesn t mean the income effect must be zero. It could be, doesn t have to be.