Question

13. The inverse demand function for cantaloupes is defined by the equation p = 305 - 5q, where q is the number of units sold. The inverse supply function is defined by p = 8 + 4q. A tax of $45 is imposed on suppliers for each unit of cantaloupes that they sell. When the tax is imposed, the quantity of cantaloupes sold falls to

A. 28.

B. 33.

C. 21.75.

D. 26.

E. 30.50.

14. The price elasticity of demand for a certain agricultural product is constant (over the relevant range of prices) and equal to -2. The supply elasticity for this product is constant and equal to 3. Originally the equilibrium price of this good was $45 per unit. Then it was discovered that consumption of this product was unhealthy. The quantity that would be demanded at any price fell by 100%. The percent change in the long-run equilibrium consumption of this good was

A. -100%.

B. -64%.

C. -20%.

D. -60%.

E. There is not enough information to determine the answer.

15. Suppose that King Kanuta, whom you met in your workbook, demands that each of his subjects give him 2 coconuts for every coconut that they consume. The king puts all of the coconuts that he collects in a large pile and burns them. The supply of coconuts is given by S(ps) = 100ps, where ps is the price received by suppliers. The demand for coconuts by the king’s subjects is given by D(pd) = 6,000 - 100pd, where pd is the price paid by consumers. In equilibrium, the price received by suppliers will be

A. $30.

B. $18.

C. $90.

D. $27.

E. None of the above

Answer 1

Ans 13.) Inverse demand equation :

P = 305 - 5q

Demand function in terms of price :

q = 61 - P/5

  

Inverse supply equation :

P = 8 + 4q

Supply function in terms of the price

q = P/4 - 2

When a tax is imposed, the price received by the seller is less than that paid by the buyer and the difference between the seller and buyer price is equal to the amount of tax.

Price_seller = Price paid_buyer - Tax

As per the given information:

Price_seller  = Price_buyer - 45

Substituting the seller price in the supply equation and then equating it to demand function gives :

(p -45)/4 - 2 = 61 - p/5

P/4 - 45/4 + P/5 = 63

(5P + 4P)/20 = 63 + 45/4

9P/20 = 297/4

9P/20 = 74.25

9P = 20 × (74.25)

9P = 1485

P = 1485/9 =165

price paid by buyer after tax = $165

Price received by seller = 165 - 45 = $120

Supply after tax :

Substituting seller price in the supply function

q = 120/4 - 2

q = 30 - 2

q = 28

Quantity sold falls to 28 units.