2. The Market research department at a nursery determines that demand for garden

Question

2. The Market research department at a nursery determines that demand for garden shrubs is given by:
Q= 1,000 - 5Ps +0.051 - 50Pt
where Ps is the price of shrubs, I is income, and Pr is the price of trees.
If Ps= $5, I=$20,000, and Pt=15,

a. Determine the quantity of shrubs demanded.

b. Compute the income elasticity for shrubs. Are Shrubs a necessity or a luxury?

c. Compute the cross elasticity for shrubs and trees. Are these two goods substitutes or complements?


3. Market Equilibrium. Various beverages are sold by roving vendors at Busch Stadium, home of the St. Louis Cardinals. Demand and supply of the product are both highly sensitive to changes in the weather. During hot summer months, demand for ice-cold beverages grows rapidly. On the other hand, hot dry weather has an adverse effect on supply in that it taxes the stamina of the vendor carrying his or her goods up and down many flights of stairs. The only competition for this service is provided by the beverages that can be purchased at kiosks located throughout the stadium.
Demand and supply functions for ice-cold beverages per game are as follows:
Qd = 20,000 - 20,000P + 7,500Pk + 0.8Y + 500T (Demand)
Qs = 1,000 + 12,000P - 900Pl - 1,000Pc - 200T (Supply)

where P is the average price of ice-cold beverage ( $ per berverage), Pk is the average price of beverages sold at the kiosks ($ per beverage), Y is disposable income per household for baseball fans, T is the average daily high temperature (Degrees), Pl is the average price of unskilled labor ($ per hour), and Pc is the average cost of capital (in percent)

A. When quantity is expressed as a function of price, what are the ice-cold beverage demand and supply functions if P=$5, Pk=$4, Y=$62,500, T= 80 degrees, Pt=$10, and Pc= 12%

B. Calculate the surplus or shortage of ice-cold beverage when P=$4

C. Calculate the market equilibrium price-output combination.

4. Give the demand function Q=100 - 0.2P, determine:

a. the total revenue equation as a function of Q.

b. The marginal revenue equation as a function of Q

C. The value of Q that maximizes total revenue. Also, the price and the point elasticity at this output rate

D. If the firm is currently charging $60, should price be increased or decreased to increase total revenue? Explain

Explanation / Answer

a) The quantity of shrubs demanded are Q = 1000 - 5($5) + 0.05($20,000) - 50(15) = 1000 - 25 + $1000 - $750 = 1,225 b) The formula for calculating the income elasticity is Income elasticity = % change in quantity demanded / % change in income If the quantity demanded wil increase by 10% then the income will change by Q = 1,225 * (1.1) = 1,347.5 Put this value in the above equation, we get 1,347.5 = 1000 - 5($5) + 0.05(I) - 50(15) $1,122.5 = 0.05 (I) $22,450 = I Therefore, with 10% increase in quantity demanded the income was increased by 12.25% Income elasticity = 0.1 / 0.1225 = 0.816 Cross elasticity = 0.1225 / 0.1 = 1.225 3) a) Qd = 20,000 - 100,000 + 30,000 + 50,000 + $40,000 = 40,000 Qs = 1,000 + 60,000 - 9,000 - 120 - 16,000 = 35,880 b) Qd = 20,000 - 80,000 + 30,000 + 50,000 + 40,000 = 60,000 Qs = 1,000 + 48,000 - 9,000 - 120 - 16,000 = 23,880 There is a shortage of the ice-cold beverage when p=$4 The demand is more than the supply. 4) a) Total revenue = P(Q) But P(Q) = 500 - Q/0.2 TR(Q) = 500Q - Q^2 / 0.2 b) MR(Q) = 500 - Q / 0.1

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