solutionproblemset7 - cars in Germany in a...

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UCLA Economics 11 – Fall 2006 Professor Mazzocco Homework 7 ANSWER KEY 1) Suppose that the cost function of X is given by: C = 100 -10X + 5X 2 a) Find the variable cost b) Find the fixed cost c) Find the average cost. d) Find the marginal cost e) Draw the relationship between MC and AC. Prove that they always intersect at the minimum AC a) VC=-10X+5X 2 b) FC=100 c) AC=100/X-10+5X d) MC=-10+10X e) Min AC = dAC/dX=0 -100/X 2 +5=0 X=20 1/2 , AC=MC 100/X-10+5X=-10+10X, X=20 1/2 2) Suppose that the cost function of a firm is given by: C(q) = 100 + 5q 2 a) Find Fixed and Variable cost. b) Find marginal cost c) Find average cost d) Draw the relationship between MC and AC. a) Fixed Cost=100, Average Cost=5q 2 b) Average cost= 100/q+5q c) Marginal cost=25q 3) Volkswagen has two plants in which it produces its cars: It can either produce
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Unformatted text preview: cars in Germany, in a high-productivity plant, or in Mexico in a lower productivity plant. The production function for cars in the German plant is Q =min(3K,2L), while the production function for cars in the Mexican plant is Q=min(K,L) a) If the wage rate in Germany is w G , and the rental rate of capital is v (the same in both countries), what is the cost function for cars in Germany (Mexico)? b) If the wage rate in Mexico is w M , and the rental rate of capital is v (the same in both countries), what is the cost function for cars in Mexico? c) Suppose capital is fixed in each country. Find the short run cost function. Answer a) C G =Q[v/3+w G /2], b) C G =Q[v+w M ] c) C G =vK G +w G Q/2, C M =vK m +w m Q...
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