Consider the generalized demand and supply functions for good X:

Qd =800-2P-0.01M+16PY

Qs = 50 + 4P - 40PI + 51F

a. Is good X normal or inferior? Explain.

b. Are goods X and Y substitutes or complements in consumption? Explain.

c. Suppose income is initially $20,000, the price of good Y is $10, the price of the input is $25, and the number of firms producing good X is 20. Write the equations for demand and supply. What is the equilibrium price and quantity?

d. Let the price of the related good Y increase to $50 and the price of the input increase to $36. Assume these two events occur simultaneously. Determine the new equilibrium price and quantity.

e. Carefully explain the changes in demand and supply as well as the changes in equilibrium price and quantity. Be sure to discuss why we ended up at the new equilibrium.

f. Sketch the demand and supply diagrams from parts c and d. Label the curves from part c D1 and S1 and those from part d D2 and S2.