Arnold consumes ketchup and celery. His utility is given by = 4^3+^4wherekis the number of pounds of ketchup andcis the number of bars of celery. He can consume ketchup and celery in any fractions he wants.

a. On Monday, the price of ketchup is $2.00/pound and the price of chocolate is $1.50/bar. Arnold has a total of $21 to spend. What is his utility maximizing combination of ketchup and celery?

b. On Tuesday, the price of ketchup falls to $1.00/pound and the price of celery stays constant at $1.50/bar. Arnold still has $21 to spend. What is his utility maximizing combination of ketchup and celery?

c. On Wednesday, the price of ketchup rises to $1.50/pound and the price of celery stays constant at $1.50/bar. Arnold still has $21 to spend. What is his utility maximizing combination of ketchup and celery?

d. Use your results from (a), (b), and (c) to sketch Arnold's demand curve for ketchup. Does it obey the law of demand? Explain.

e. Find an expression for Arnold's demand for ketchup as a function of pc, pk, and I. (hint: solve the problem in the exact way you have done it before but use general prices (pc, pk) and income (I) rather than specific values). Does this expression obey the law of demand?

f. Arnold's friend Cedric has the demand K=20-.5Pk-.4I+.2Pc. Is Ketchup a normal or inferior good for Cedric? How do you know?