# Economics 212 Microeconomic Theory I Final Exam. June Faculty of Arts and Sciences Queen s University Answer Key

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1 Instuctions Economics 1 Micoeconomic Theoy I Final Exam June 008 Faculty of Ats and Sciences ueen s Univesity Anse Key The exam is thee hous in length. The exam consists of to sections: Section A has five shot questions and is oth 5 maks (5 maks each) and Section B has five poblems and is oth 75 maks (15 maks each). Please ite you anses in the space povided in this booklet. You may do ough ok on the back of the pages o continue an anse thee if you un out of space. Please indicate that you anse continues on the back of the page. Fo full maks you must coectly deive you anses and sho all you ok. Please ite you student numbe in the space belo. Note: Poctos ae unable to espond to queies about the intepetation of exam questions. Do you best to anse the exam questions as itten. STUDENT NUMBER:

2 A1. Accoding to the folloing diagam, hat is the deadeight loss unde monopoly? Hint: compute consume suplus and poduce suplus unde pefect competition and monopoly then compae. Pice MC MR D uantity The pofit-maximizing pice fo a pefectly competitive fim ould be 10. The pofit-maximizing pice fo a monopolist ould be 40. The total economic benefit unde pefect competition ould be 1350 The total economic benefit unde monopoly ould be 100. The deadeight loss unde monopoly ould be 150.

3 A. When a poduction function can be expessed as ( ak)( bl), the elationship beteen capital and labo in the poduction function is that capital and labou ae easily substituted, and the isoquants ae convex to the oigin. Tue. A3. Conside the total cost cuve TC At hat level of does aveage cost each a minimum? Does this total cost function exhibit economies of scale, diseconomies of scale, o neithe? MC Aveage cost eaches a minimum at the point hee aveage cost and maginal cost intesect. Aveage cost is TC AC AC AC No set AC MC to find the minimum of aveage cost Thus, aveage cost eaches a minimum at 0. To detemine hethe this has economies o diseconomies of scale, calculate the output elasticity of total cost. MC εtc, AC εtc, hich fo any positive level of output ill be geate than one. This implies the total cost function exhibits diseconomies of scale.

4 A4. The maket fo seet potatoes consists of 1,000 identical fims. The maket demand cuve is given by 40 P. Each fim has a shot-un total cost cuve of STC Deive the shot-un quantity supplied by each individual fim? Will the fim ean a shot-un pofit, a shot-un loss, zeo economic pofit o a long-un pofit? Explain. Each fim has a shot-un maginal cost cuve of SMC 00. Each fim has an aveage vaiable cost cuve of AVC 100. Each individual fim ill supply The fim ill ean a shot-un pofit. A5. Suppose demand fo a monopolist s poduct is given by P hile the monopolist s maginal cost is given by MC 3. What ae the pofit-maximizing quantity of output and pice fo this monopolist? If the govenment imposes a tax of \$15 pe unit, ho much the monopolist ill chage in this case? Ho many units he ill supply? MRMC MR Solve to get 0 and P180. The monopolist vies the tax as an incease in his/he maginal cost, so the ule is no MRMC + t Solve to get, t18 and Pt19

5 Section B: Five poblems, each oth 15 maks, fo a total of 75 maks. Each pat of each question oth five maks. B1. Suppose a pefectly competitive fim has the poduction function 10K L, hee is output, L is labou and K is capital. The age ate is pe hou and the ental ate of capital is. a) Deive the conditional input demand functions of the fim? MP L 0K L and MP K 0KL. Use the tangency condition to detemine the optimal capital-labo atio. MPL MPK 0K L 0KL K L K L (1) Next substitute into the poduction function 4 10 ( L ) L 10 L ( ) 4 L ( ) 10 1 / 4 1 / * L 10 * Substitute L into (1) e get K * L * 10 1/ 4 b) Deive the long-un total cost function fo the fim. 1/ 1/ 4 * * C L + K 10 1/ 4 1/ 1/ Reaanging, e get 1/ 4 1/ 1/ The cost cuve ill be concave / C * 1/ 4 1/ 1/ 4 1/ 1/ 10

6 c) If the age ate is \$0 pe unit of labou and the ental ate of capital is \$100 pe unit, ho much capital and labou should the fim employ in the long un to maximize output hile spending exactly \$10,000? Use the tangency condition to detemine the optimal capital-labou atio. MPL MP K 0K L 0 0KL 100 K 1 L 5 L 5K Next, use this esult ith the cost function to detemine the optimal quantities of capital and labou. TC L + K 10, 000 0L+ 100K 10, 000 0( 5K) + 100K 10, K + 100K 00K K 50 L 50 Ho much output can the fim poduce? 10K L 10(50) (50) 1,56,500,000 B. In a cetain maket in the long-un, each fim and potential entant has a long-un cost 3 cuve C( ) hee is thousands of units pe yea. Maket demand is given by DP ( ) 39,000,000P. a) Solve fo the long-un equilibium output pe fim, maket pice, numbe of fims and maket output? In the long-un equilibium, each fim ill poduce hee P AC MC. Thus, Since each fim poduces hee P MC, pice ill be

7 P P + 30(0.5) 10(0.5) 0 P Substitute P in the maket demand e get the maket output * 39,000, Since total maket demand is 50 and each fim is poduce 0.5 units, the total numbe of fims in the maket in equilibium ill be 50 N 0.5 N 1,000 b) Suppose a technological innovation educes the fims cost cuves to 3 C( ) Sho ho this affects the equilibium values deived in pat a). In the long-un equilibium, each fim ill poduce hee P AC MC. Thus, Solving fo e get 0.3. Substitute in the MC to get P (PMC), P19.1 Substitute P in the maket demand e get the maket output * 39,000, And the total numbe of fims in the equilibium is n800/ c) Suppose that the fims in this question poduce using a technology that displays inceasing etuns to scale ove the entie ange of output. Sketch the long-un aveage and maginal cost cuves. What issues aise in detemining the long-un equilibium in the maket?

8 d B3. In a paticula U.S. maket, quantity demanded is given by 500 0P and s quantity supplied is given by P. The old pice fo this poduct is \$6, and an unlimited amount can be puchased at this pice. a) With impots pohibited by the U.S., hat is the domestic equilibium pice and quantity? d s With impots pohibited, simply set. This yields 500 0P P 50P 450 P 9 At this pice, the domestic quantity sold ill be 500 0(9) 30. b) No suppose the govenment opens up the U.S. economy to fee tade. Ho ill this affect the equilibium maket pice, the quantity supplied by domestic supplies, the quantity puchased by domestic consumes, and the level of impots? When the govenment opens up the economy to fee tade, the equilibium pice ill fall to the old pice, \$6. At this pice, domestic consumes ill demand d s 500 0(6) 380 units and domestic supplies ill povide (6) 30 units. Impots ill be the diffeence, o 150 units.

9 c) Finally, suppose the govenment sets a taiff of \$ pe unit. Ho ill this affect the equilibium maket pice, the quantity supplied by domestic supplies, the quantity puchased by domestic consumes, and the level of impots? When the govenment imposes the taiff of \$ pe unit, the pice ill ise fom \$6 to \$8, still belo the closed-economy equilibium. At this pice, domestic consumes ill d demand 500 0(8) 340 units and domestic supplies ill povide s (8) 90 units. Impots ill be the diffeence, o 50 units. Taiff evenue is B4. A homogeneous poducts duopoly faces a maket demand function given by P Fim 1 has a constant maginal cost MC 50. Fim has a constant maginal cost MC 60. a) What ae the Counot equilibium quantities and industy pice? Find Fim s eaction function by setting MR MC. ( ) Find Fim 1 s eaction function by setting MR MC. ( ) Then solve the to eaction functions simultaneously ( 0.5 1) The industy pice is P

10 b) If fim 1 has the advantage of making its output choice fist (leade), hat ould be the equilibium quantities and the maket pice in this case? We kno that Plug this in total etun function fo fim 1, e get TR1 P( 1 + ) ( ) And the maginal etun ill be MR Setting this equal to MC (50) and solve e get 1 3. Substitute this in e get It follos that P 500 ( ) 155 c) No suppose that fim 1 buys fim and acts as a monopolist in the maket. The ne fim decides to poduce using only the plant of fim. Solve fo the equilibium values of pice and output? Did the ne fim maximize pofits? Explain. The ule is MRMC. Note hee the fim is unning plant only ith MC60. TR P( ) MR MC Which hen solving fo e get. Subsituting in the invese demand function to get the pice, P80. The fim is not maximizing its pofit because it is using the plant ith the highe maginal cost. It ould be moe pofitable to the fim if it uses plant 1, ith loe maginal cost, MC 1 50 < MC 60.

11 B5. Conside the folloing to-playe game. Playe 1 Playe B 1 B B 3 A 1 15, 10, 8 6, 4 A 9, 3 5, 7 3, 1 A 3 1, 3 9, 8 17, 7 a) Does eithe Playe have a dominant stategy? A dominated stategy? Find the Nash Equilibium (equilibia, if any) fo this game. b) If Playe 1 gets to choose fist, afte hich Playe ill choose. Da the game in extended fom (game tee). What is the outcome of this game? Explain you easoning. Is the equilibium diffeent fom the one deived in pat a).

12 c) Would it be possible fo playe 1 to bibe playe to obtain an outcome that is bette fo both playes? Explain.

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