Examination 2 Fall 2005

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1 Economics 5 Eamination Fall 5 A. Key. Consider a market with linear demand as illustrated below: $ 8 Demand 4 5,,5 Q a) s demand elastic, inelastic, or unit elastic at a rice of = 5? Elain. (6 oints) For a linear demand curve, demand is inelastic along the bottom half of the curve. Therefore, for the demand function illustrated above, demand is inelastic at a rice of = 5 (since < () = 6 ). 5 b) Would an increase rice from = 7 to = 9 result in an increase, decrease, or no change in total eenditures on this good? Elain. (6 oints) For the linear demand illustrated above, demand is elastic for all rices above 6 = (). n general, as rice is increased along an elastic ortion of a demand curve, total eenditures will decrease. Thus, increasing rice from = 7 to = 9 would result in a decrease in total eenditures on this good. c) Suose rice were to decrease from = 8 to = 4. Determine the value of the resulting increase in Consumer s Surlus. (6 oints) As rice is decreased from = 8 to = 4, quantity demanded increases from q = 5 to q =,. Since demand is linear, the resulting increase in Consumers Surlus is: CS = 8 4)(5 ) + (, 5)(8 4) =, +, = 3,. (

2 . The following elasticities have been estimated for Product X and Product Y under current market conditions: Elasticity Product X Product Y Price Elasticity of Demand.9.37 Cross-Price Elasticity of Demand ncome Elasticity of Demand Based uon these estimates, answer the following questions. a) Would an increase in the rice of Product X lead to an increase, decrease, or no change in total eenditures on Product X? Elain, making secific reference to one of the si values given above. (4 oints) Under current market conditions, demand for X is inelastic (since. 9 < ). Therefore, an increase in the rice of X would lead to increased eenditure on X. b) Would an increase in the rice of Product X lead to an increase or a decrease in the demand for Product Y? Elain, making secific reference to one of the si values given above. (4 oints) Since the cross-rice elasticity of demand for Y with resect to the rice of X is negative (. < ), we can infer that an increase in the rice of X would lead to a decrease in demand for Y. c) Would an increase in consumer income lead to an increase or a decrease in the demand for Product X? Elain, making secific reference to one of the si values given above. (4 oints) Since the income elasticity of demand for X is negative (. 5 < ), we can infer that an increase in consumer income would lead to a decrease in demand for X. d) s Product Y a normal good or an inferior good? Elain, making secific reference to one of the si values given above. (4 oints) Since the income elasticity of demand for Y is ositive (. 34 > ), we can infer that an increase in consumer income would lead to an increase in demand for Y. Therefore, Y is a normal good.

3 3. Consider a erfectly cometitive firm oerating in the Short Run. The only factor of roduction that is variable is the amount of labor hired, denoted (L). The first two columns of the table below secify the relation between (L) and outut roduced (Q). MPL denotes the Marginal Product of Labor; MC denotes Marginal Costs of Production. Suose that: the Average Variable Costs of roducing units of outut are 4; the Average Fied Costs of roducing units of outut are ; the rice of the outut of this firm is = 3 er unit. L Q MPL MC a) Comlete the table above (filling in ALL blank cells). (5 oints) Note: Since the Average Variable Costs of roducing units of outut are 4, it follows that the Variable Costs of roducing units of outut by way of hiring unit of labor are 4. Therefore, w = 4. MPL is simly equal to the increase in Q; MC is equal to w MPL. b) Determine the otimal amount of outut for this firm to roduce. Elain. (5 oints) Note that MR = = 3. The firm should hire L = 4 units of labor, since u to this level MC < MR while beyond this level MC > MR. This choice results in Q = units of outut being roduced. c) Determine the maimum rofit that this firm is able to earn. Elain. (6 oints) Since Average Fied Costs of roducing units of outut are, it follows that F = 44. n general, rofit can be eressed as π = q VC( F. For L = 4 and Q = this is equal to π = (3) (4)4 44 = = 3.

4 4. The budget line below reresents all combinations of ocorn and retzels that Rebecca can buy with a fied amount of income. Suose the er unit rice of retzels is =. 3 retzels Budget Line ocorn a) How much income does Rebecca have to send on these two goods? Clearly elain. (4 oints) = 3 imlies 3 =. t follows that = 6. b) What is the er unit rice of ocorn? Clearly elain. (4 oints) 6 =. Since = 6, this imlies = 6 = =.. From here, c) Suose that Rebecca s income were to double (with rices fied). llustrate her new budget line, clearly labeling the value of each intercet, as well as the sloe of the line. (4 oints) retzels 6 Sloe = = 4 ocorn 4

5 5. Consider a erfectly cometitive firm oerating in the Short Run. Marginal Costs, Average Variable Costs, and Average Total Costs are illustrated below. $ ATC 3 MC 8 AVC 6 q 4 8 a) Suose the rice of the outut of this firm is = 3. s this firm able to earn a ositive rofit at this rice? Elain. (6 oints) Yes. Note that ATC = min 8. Since > ATCmin, there are values of q for which q > TC(. Such values result in ositive rofit. b) Suose the rice of the outut of this firm is =. What quantity of outut should this firm roduce in order to maimize rofit? How much rofit is this firm able to earn? Elain. (6 oints) For =, we have > AVC = min. Therefore, the firm will want to choose q so that MC ( =. From the grah above, this rofit maimizing level of outut is q = 4. This level of roduction leads to rofit of = q qatc( = q[ ATC( ] = 4[ 3] = (48) π. c) f the firm were to roduce units of outut, what would be the realized value of Fied Costs of roduction? Elain. (6 oints) For any level of outut, AFC( = ATC( AVC(. From the grah above, this allows us to determine that AFC ( 4) = 6 and AFC ( 8) = 8. From either of these values, it follows that F = 64. By definition, Fied Costs do not deend uon the level of outut, imlying that the realized Fied Costs when roducing units of outut would be F = 64.

6 6. Gene s references for =(blue t-shirts) and =(cigarettes) can be summarized by u ( X ) = 4. As a result, his marginal utility functions are = and =. Suose each unit of costs, each unit of costs, and Gene s income is equal to. a) llustrate the indifference curve along which Gene realizes utility of u = 4. dentify three different consumtion bundles along this curve. (6 oints) cigarettes u = 4 A consumtion bundle is on this curve if and only if eamle: (,8), ( 6,6), and ( 8,). b) Derive an eression for MRS,. (6 oints) Blue t-shirts 36 =. For MRS =, =. c) Showing all work, determine Gene s otimal levels of consumtion as functions of,, and. (8 oints) The otimal bundle is the unique (, ) for which the following conditions hold simultaneously: + = and = MRS. The, second condition imlies =. This insight, along with the first condition gives us (,, ) =. From here, (,, ) =.

7 EXTRA CREDT - 3 Points! Consider a market in which demand is given by D( ) = (for 36 ). Price elasticity of demand is given by ε = eenditures in this market maimized? Elain.. At what rice are total n order for total eenditures to be maimized, it must be that ε =. From the eression above, this requires: = = 3 = = 4 = 6

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