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  3. 1 suppose that alex must produce his own cereal using...

Question: 1 suppose that alex must produce his own cereal using...

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1. Suppose that Alex must produce his own cereal, using inputs of raw materials obtained from his parents food storage (S) and labor provided by Alexs cook- ing skills (L). Production of cereal is given by Fc(LS)-L0.5S0.5. Further. suppose Alex has a utility function Ua(ca,Ca) c505, where ca is his consump- tion of cereal and la is the amount of leisure he enjoys. He has no endowment of cereal, but is endowed with 120 hours of time (which can be sold as labor or kept as leisure) and 40 food storage cans (s) (a) (2 pts) Set up Alexs household problem (b) (2 pts) Alex creates a firm to produce cereal. Set up the firms problem (c) (4 pts) Define a competitive equilibrium for this economy. (You may refer to the previous two parts as appropriate, rather than repeating them, but be precise.) Be sure to specify the market clearing condition for each market (d) (4 pts) Solve for the aggregate (i.e. Alexs) demand for leisure and for there should be no other cereal (in terms of input and output prices variables in the resulting equations) You should get c120p40p 2pe and 120pe+40pII 2pe (e) (4 pts) Solve the firms problem Remember that with CRS production, this will just pin down rel ative prices, not give you solutions for C and L. You should get 4pe (f) (4 pts) The previous question gives a profit-maximizing relationship be- tween S and L (in macro, this is called the capital-to-labor ratio). Use this to substitute for L in the production function, and simplify to get the supply of C as a function of input S. Also, compute the profit earned given S 2 GE Production 0.5 You should get C- ) S and 11-0. (Others can be found. but are equivalent if you substitute using the price relationship from the previous problem.) (g) (3 pts) Solve for the equilibrium prices Normalizing the price of cereal to 1 mαy be easiest. This looks messy at first, but you should get p- and p- (h) (2 pts) Solve for the equilibrium allocation You should get c*ー40,(*ー80. L* = 40. S* = 40, C* 40

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