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 frm 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 frm experiences an increase in FC. Aren’t my graphs nice? I did them in Matlab. Of course, Excel is probably just as good–but not as hard. Notice that the new average 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 frm 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) 1

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The frm will experience increased fxed costs and decreased marginal costs simultaneously: Notice that AC 1 crosses AC 2 q . 2. Suppose that individuals in a market have demand P = 50 - q/ 5 , and that frms 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 frms 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 p 50 - 755 16 P 675 4 = 30375 128 s 237 . 3 PS = 1 2 p 755 16 - 5 P 675 4 = 455625 128 s 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? Solving elasticity for price, and letting

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

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