Practice Problems 100 A Midterm 1 Practice The

Practice Problems 100 A Midterm #1

Practice The inverse demand curve for product X is given by: l Px = 25 - 0. 005 Q + 0. 15 Py, l where PX represents price in dollars per unit, Q represents rate of sales in pounds per week, and Py represents selling price of another product Y in dollars per unit. The inverse supply curve of product X is given by: l Px = 5 + 0. 004 Q. l Determine the equilibrium price and sales of X. Let Py = $10. l Determine whether X and Y are substitutes or complements.

Solution: l l l Equate supply to demand to calculate Q. 25 - 0. 005 Q + 0. 15(10) = 5 + 0. 004 Q 21. 5 = 0. 009 Q Q = 2, 388. 9 units per week At Q = 2, 388. 9, P = 25 -. 005(2, 388. 9) + 0. 15(10) = $14. 56 per unit.

Solution l l Since we can solve for quantity demanded as a function of prices, we see that there is a direct, positive relationship between Q and Py. (Q = 25+. 15 Py-Px)/. 005 Increases in the price of good Y raise the quantity demanded for good X at any value of Px. This implies that goods Y and X are substitutes.

Practice l l Mid-continent Plastics makes 80 fiberglass truck hoods per day for large truck manufacturers. Each hood sells for $500. Mid-continent sells all of its product to the large truck manufacturers. If the own price elasticity of demand for hoods is ‑ 0. 4 and the price elasticity of supply is 1. 5: Compute the supply and demand for truck hoods.

Solution l l l l l Given: P* = $500 Q* = 80 hoods per day Ed = -0. 40 Es = 1. 5 Demand: Qd = a + b. P Supply: Qs = c + d. P Use E = P/Q(ΔQ/ΔP) to compute b and d. b = -0. 064 d = 0. 24 Solve for a and c Qd = a + b. P Qs = c + d. P 80 = a + -0. 064(500) 80 = c + 0. 24(500) a = 112 c = -40 Qd = 112 - 0. 064 P Qs = -40 + 0. 24 P