# Demand and Supply in Competitive Markets

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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?

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##### Solution Summary

The demand and supply for competitive markets are examined.

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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 = ...

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