Suppose that the demand equation for widgets is Q = 10,000 − 25P.

a. How many widgets will be sold for $100?

b. At what price will the demand for widgets zero?

c. What is the total revenue equation for widgets in terms of output?

What is the marginal revenue equation in terms of output?

d. What is the price elasticity of demand when P = $200? What is the firm’s total and marginal revenue at this price?

e. What is the price elasticity of demand if the price of widgets falls to P = $150? At this price what is the firm’s total and marginal revenue? Explain your results.

f. What is the price elasticity of demand if the price of widgets rises to P = $250? At this price what is the firm’s total and marginal revenue? Explain your results.

g. Suppose that the supply of widgets is given by the equation Q = −5,000 + 50P.

What is the equilibrium price and quantity?

h. What is the relationship between quantity supplied and quantity demanded at P = $300?