Econ 30223 Homework 3 Optimization

Econ 30223 Homework 3 Optimization in $8 only

Instructions. Answer each question on your own paper. Turn in this cover sheet on top of your answers (in the correct order, please) stapled together. The due date is above and remember, I cannot accept late work.

1. I buy only purple shirts (S) and frogs (F ) and have income I. My budget constraint is I = PS S +PF F . For each case, solve the consumer choice problem: …nd my demand for shirts and frogs as functions of market prices and incomes. (so for part a, b, and c below …nd the Marshallian demand functions).
(a) My utility function is U (S; F ) = 3S + 7F:
(b) My utility function is U (S; F ) = min

2 S; 8 F:

(c) My utility function is U (S; F ) = 2 ln(S) + ln(F ):
2. Fred has $20. His utility from dino-burgers (D) and pterodactyl drumsticks (T ) is U (D; T ) = D + 2 T .

(a) Prices are $1 each for both D and T . What bundle does Fred choose? What’ his utility?
(b) The price of dino-burgers has gone up to $2.50 as dinosaurs have become harder to …nd. (Apparently, pterodactyls are technically not dinosaurs.) What bundle does Fred choose now? What’s his utility?
(c) Draw a diagram with both budget constraints and both indi¤erence curves. Mark Fred’ optimals bundles for each part. MAKE YOUR ICs IN DASHED LINES so I can distinguish them from the BCs. Put D on the horizontal axis.
3. Are any points on a Marshallian demand curve not the consumer’ optimal choice? Why or why not?
4. Consider the function f (x; y) = x0:25 y 0:75 . Find the values of x and y that maximize this function subject to the constraint 4x + 8y = 24.
5. Consider the function f (x; y) = 3xy

y 2 , with a constraint of x + y = 48. Solve the Lagrangian.

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