Question

Dizzy Inc. is the only operator of themed amusement parks (DizzyWorld). Dizzy’s production function (which, oddly, relies only on labor) is given by:

Q = 60L^0.5

Dizzy pays its workers w = $12. Consumer demand for admission to DizzyWorld is given by: QD = 24,000 – 200P

1a) Find Dizzy Inc’s profit-maximizing quantity (number of theme park admissions)

1b)  Find what price Dizzy will charge to attain this level of demand?

1c)  Compare (using SPECIFIC NUMBERS) the Monopoly P and Q with the outcomes form a perfectly competitive market

Answer 1

For Monopolist, Profit maximizing condition is MR=MC

1a) For MC:

MC= W/Marginal product of labor

Marginal product of labor= dQ/dL= 30/(L)0.5

MC= 12/(30/(L)0.5)= 12L0.5/30

From production function:

L0.5=Q/60

MC= 12(Q)/30*60= Q/150

For MR:

QD = 24,000 – 200P

P= (24000-QD) / 200 (AR)

TR= P*QD= (24000QD-QD2)/200

MR= (24000-2QD)/200

Now put MR=MC

(24000-2QD)/200 = Q/150

3600000-300Q= 200Q

Q= 7200 Profit maximizing quantity.

1b) P= (24000-QD) / 200

P= (24000-7200)/200= 84

1c) In perfect competiton:

AR=MC

(24000-QD) / 200 = Q/150

3600000-150Q=200Q

3600000=350Q

Q=10286 (approx)

P= 24000-10286 / 200= 68.57

In perfect competiton a firm is selling higher quantity at a lower price as compare to monopoly.