My tastes for chocolate (x) and other goods (y) can be represented by the utility function u( x,y) = 9x^2/3 + y , where MUx = 6 / x^1/3 and MUy = 1.
a) State the optimization problem. What are the endogenous variables in this problem? Exogenous variables?
b) Calculate my optimal consumption of chocolate and other goods as a function of all exogenous variables. That is, derive demand for chocolate and demand for the other goods.h) What information does a demand functions from part b) impart? Is there anything unusual about this demand functions? Calculate cross-price elasticity of demand for chocolate. Are these goods substitutes or complements?
c) Calculate my optimal consumption of chocolate for income of $24 when price of a chocolate is $3 and py is $1.
d) Calculate my optimal consumption of chocolate when income increases to $30per week.
e) On a graph with weekly chocolate consumption on the horizontal and "other goods" on the vertical, illustrate my optimal consumption when my weekly income is $24 and when my weekly income is $30
f) From what you observed thus far, is chocolate a normal or an inferior good for me? Compute my income elasticity of demand.g) Assume that my income remains $24 per week and the price of chocolate falls to$2.00 Calculate and illustrate my new optimal consumption bundle. (Note this part is challenging).