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# ps3 - as well as capital k GM’s production function is x...

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Problem Set 3 Due Thursday, Oct. 15th, by 10pm 1. Andrew and Daniel consume bionicles ( x 1 ) and superhero costumes ( x 2 ). Andrew starts off with 10 bionicles while Daniel starts off with 10 costumes. Andrew’s utility function is u A = 5 ln( x A 1 ) + x A 2 while Daniel’s utility function is u D = x D 1 x D 2 (a) Draw an Edgeworth box that represents their current endowments. Be sure to label all relevant points. (b) Derive Andrew and Daniel’s demands as a function of p 1 /p 2 . (c) Find the market clearing price. (d) Find two points that are Pareto efficient 2. GM produces cars, x , using two types of labor, l 1 and l 2
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Unformatted text preview: , as well as capital, k . GM’s production function is x = min n l 1 / 3 1 l 1 / 3 2 ,k o . The price of cars is p and the input prices are w 1 , w 2 , and r . In the short run, GM’s capital level is ﬁxed at k . (a) Find GM’s short run input demands for l 1 and l 2 . (b) Derive GM’s short run proﬁt function. (c) Find GM’s long run input demands for l 1 , l 2 , and k . (d) Derive GM’s long run proﬁt function. (e) Suppose the government decides to bailout GM by giving them B dollars. How does B aﬀect GM’s decisions? 1...
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