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ps2f06s

# ps2f06s - Economics 101 Problem Set 2 Alan C Marco...

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Economics 101, Problem Set 2 Alan C. Marco Solutions Solutions. 1. A firm has upward sloping MC and some FC . Using a graph, show the impact on the MC curve and AC curve of the following changes. In each graph show the old MC and AC curves as well as the new ones. (a) The firm experiences an increase in FC. Aren’t my graphs nice? I didtheminMatlab. Ofcourse, Excelisprobably justas good–butnot ashard. Notice that the newaverage cost curve approaches the old one as q gets larger. This is b/c FC gets spread over more units. Also note that the minimum of AC is still where AC=MC. (b) The firm experiences a \$1 increase in MC (every unit now costs \$1 more to produce). Note that this is a “parallel” shift in AC and MC. They all shift up by \$1. (c) The firm invests in R&D in order to lower its costs of production. 1

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The firm will experience increased fixed costs and decreased marginal costs simultaneously: Notice that AC 1 crosses AC 2 so that R&D to reduce marginal costs makes sense only for large q . 2. Suppose that individuals in a market have demand P =50 - q/ 5 , and that firms have marginal costs MC = 5+2 q. (a) If there are 12 individuals in the market, what is the market demand? Individual demand can be written as q =5(50 - P ) So market demand is Q =12 q =60(50 - P ) or P =50 - Q 60 (b) If there are 8 identical firms in the market, what is market supply? Individual supply can be written as q = 1 2 ( P - 5) So market supply is Q =8 q =4( P - 5) or P =5+ Q 4 (c) What is the equilibrium of this market? We have two equations and two unknowns: P = 50 - Q 60 P = 5+ Q 4 Solving these, we get Q * = 675 4 ,P * = 755 16 2
(d) At the equilibrium what are the price elasticity of demand and the price elasticity of supply? The elasticity of demand is given by ε = - 1 slope P Q D =60 755 16 675 4 = 151 9 The elasticity of supply is given by η = 1 slope P Q S =4 755 16 675 4 = 151 135 (e) At the equilibrium, what is consumer surplus and producer surplus? CS = 1 2 parenleftbigg 50 - 755 16 parenrightbigg 675 4 = 30375 128 similarequal 237 . 3 PS = 1 2 parenleftbigg 755 16 - 5 parenrightbigg 675 4 = 455625 128 similarequal 3559 . 6 3. Assume the demand curve for a good is given by P =100 - 2 Q . Suppose the demand curve shifts leftward to become P =80 - 2 Q. (a) Draw the two demand curves, with appropriate labeling. The solid curve is the original curve P =100 - 2 Q 50 45 40 35 30 25 20 15 10 5 0 100 90 80 70 60 50 40 30 20 10 0 x y (b) What happens to the price elasticity of demand at any given price?

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