Steve’s preferences for hamburgers (X) and chicken sandwiches (Y) can be represented by u(X,Y)=X 0.5Y 0.5.
a) If the price of a can of a hamburger is pX, the price of a chicken sandwich is pY, and Steve’s monthly budget for fast food is w, derive Steve’s monthly demand functions for hamburgers X(pX,pY,w) and chicken sandwiches Y(pX,pY,w). Start by stating Steve’s maximization problem.
b) What would Steve consume if pX=$10, pY=$7.50 and w=$300?
c) An outbreak of mad cow disease reduces the local supply of beef. Imported beef is more expensive, driving up the price of hamburgers to $15. How many hamburgers and chicken sandwiches does Steve now consume?
d) Graphically decompose the total effect of the price change into an income effect and substitution effect. Plot hamburger consumption on the horizontal axis. Label clearly.
e) Are hamburgers a normal or inferior good? Explain.