The current price of wheat is $1.00 per bushel, and the price elasticity of demand for wheat is known to be 0.50. A bad harvest causes the supply of wheat to decrease and as a result the price of wheat rises by 20%. What will be the percentage change in quantity demanded for wheat and will farm revenues rise or fall?

demand will fall by 10%

and revenue increase by 8%

Explanation:

the price elasticity is the relationship between the quantity demanded and the change in price:

demandQ / ΔPrice = price-elasticity

demandQ / 20% = 0.5

Qd = 20% x 0.5 = 10% the demand will fall by 10%

Now, we can determinate the revenue:

QXP = TR

Qx1 = 1Q

after the price increase:

(1 - 0.1) Q x 1.2 = 0.9 x 1.2Q = 1.08Q

1.08Q > 1Q the total revenue should increase.