# Demand and Supply in Competitive Markets

The market for hog hats is competitive and demand is given by P=75-Q while supply is given by P=15+2Q. What are the equilibrium price and quantity in this market?

Calculate the elasticity of demand at a price of 50. Give an economic interpretation to your answer. Is demand elastic, unit elastic or inelastic at this price?

To enable more students to wear hog hats to games, the UA decides to give hog hat producers a subsidy of $9 per unit. What price will consumer's pay and how many hog hats will they buy? How much will the UA spend on the subsidy? What will be the change in producer surplus?

Â© BrainMass Inc. brainmass.com October 3, 2022, 11:08 pm ad1c9bdddfhttps://brainmass.com/economics/general-equilibrium/demand-supply-competitive-markets-456769

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Demand curve is given by P = 75 - Q

Supply curve is given by P = 15 + 2Q

At the equilibrium the two curves intersect. We can find this by solving

75 - Q = 15 + 2Q

or, 75 - Q + Q = 15 + 2Q + Q

or, 75 = 15 + 3Q

or, 75 - 15 = 15 + 3Q - 15

or, 60 = 3Q

or, 20 = Q.

Thus equilibrium quantity is 20. Equilibrium price can be obtained by plugging this quantity into either the demand or the supply curve. Plug Q = 20 in the demand curve, and we get P = 75 - 20 = 55. You can verify this is the right price by plugging Q = 20 in the supply curve to get P = 15 + 2Q = 15 + (2*20) = 55.

Price elasticity of demand is calculated using the formula

PED = (1/Slope of Demand Curve)*(P/Q).

The slope of the demand curve is -1. At P = 50, quantity demanded can be found by plugging P = 50 in the demand curve. This gives us 50 = 75 - Q, or Q = 25. Thus price elasticity of demand is

PED = (1/-1)*(50/25) = -2.

We take its absolute value to say the elasticity is 2.

A subsidy shifts the supply curve to the right. Given that the supply curve was P = 15 + 2Q, the new supply curve with a subsidy of $9 per unit would be P = 6 + 2Q. The demand curve is still P = 75 - Q. As earlier we solve to find the new equilibrium:

75 - Q = 6 + 2Q

or, 75 - Q + Q = 6 + 2Q + Q

or, 75 = 6 + 3Q

or, 75 - 6 = 6 + 3Q - 6

or, 69 = 3Q

or, 23 = Q.

Plug into the demand curve to get the price as 52. Thus the new price is $52 and quantity is 23. Producers will get an additional $9 per unit. Hence they get $61 for each hog hat.

Total subsidy is number of units sold times the subsidy per unit. Number of units sold is 23 and subsidy per unit is $9 so total subsidy is 23*9 = $207.

To find the change in producer surplus we will have to draw the demand and supply curves for both cases: with and without subsidy. See the attached graph. In the graph W2A is the old supply curve, W2A - Z is the new supply curve where Z is the subsidy. Qo is the old equilibrium quantity (20), and Qn is the new equilibrium quantity (23). Po is the old price ($55), Pn is the new price paid by the consumer ($52) and Pn + Z is the new price received by the producer ($61). Area (A + B + C) is the amount of subsidy ($207). Area A is the increase in producer surplus, area B is the increase in consumer surplus, and area C is the deadweight loss.

Area A can be found out as the sum of the rectangle and triangle over the old equilibrium price. The rectangle has sides 6 ($61 - $55) and 20 (old equilibrium quantity). The triangle to the right has sides 6 ($61 - $55) and 3 (new equilibrium quantity - old equilibrium quantity). The area of the rectangle is thus 20*6 = 120, and that of the triangle is 0.5*6*3 = 9. So total area of Area A is 129. This is the change in producer surplus.

Similarly the change in consumer surplus is 64.5 and the deadweight loss is 13.5. Total subsidy is the sum of change in consumer surplus, producer surplus and deadweight loss (64.5 + 129 + 13.5 = 209).

Â© BrainMass Inc. brainmass.com October 3, 2022, 11:08 pm ad1c9bdddf>https://brainmass.com/economics/general-equilibrium/demand-supply-competitive-markets-456769