Jack receives satisfaction(utility) from eating Lobster(L) and eating meat(M). He has an income of $1,000 and spends 25% of it in lobster and meat. The price of a pound of lobster is $50 and the price of a pound of meat is $10. Suppose that economists derive jack's utility function U = L1/2M1/2 using the theory of revealed preferences. Using Jason's utility function, the economists find the marginal rate of substitution between lobster and meet is MRSLM=-L/M
a) Write down the mathematical equation for Jack's budget constraint(BC). Rewrite the BC as a function of M
b) Find the optimal consumption bundle of lobster and meat for Jack. What is his level of utility at this bundle? Using Jack's utility at this bundle, find the utility curve equation as a function of M
c) Due to a great fishing season in Maine, the price of veal decreases to $25. Write down Jack's new BC. Then solve for the optimal bundle with the new price. What is his level of utility now?
d) Using the information from part b and c, find Jack's substitution and income effect for lobster. Is lobster a normal good or an inferior good
e) Graph Jack's consumption decision before and after the price changes. Show all curves(BCs, Us), label all the intercepts, also label all the quantities L & M and the substitution and income effect for lobster
f) Using the change in price and quantity of lobster, graph Jack's demand curve. From the two points used to graph the demand curve, derive Jack's demand function of the form P = a+bQd. Now rewrite the demand function as a function of P.