Time Series and Demand and cost function

Question

1. A firm has estimated its demand function to be:

QD=2000-1000P

TC=150 0.25Q

Find the optimal price, output and profit.

2. The demand and cost function for a company are estimated to be as follows:

P=100-8Q

TC=50 80Q-10Q² 0.6Q³

A)Find the price that the firm should charge if it wishes to maximise profits in the short run.

b) The price if it wishes to maximise revenue in the short run,

3.Why is it unlikely that a firm would sell at a price of output where its demand curve is price inelastic?

4. The economists for Grant Corporation has established the company’s transportation using time series data to be

TC=50 16Q-2Q² 0.2Q³

A) Plot the curve for quantities 1 to 10 (Think u have to create ur own data here, idk)

B) Calculate the AVC and MC for these quantities and plot them another graph.

C) Discuss your results in terms of decreasing, constant and increasing Marginal Cost (MC).

Does Grant’s cost function illustrates all of these?

Is there any website I can use, Econs is not my thing so pls help!!

Answer 1

1:

Q=2000-1000P

1000P=2000-Q

P=2-0.001Q

TR=Q*P=2Q-0.001Q²

MR=(TR)'=2-0.002Q

TC=150+0.25Q

MC=(TC)'=0.25

MR=MC

2-0.002Q=0.25

1.75=0.002Q

Q=875

P=2-0.001Q= 1.125

TR=1.125*875= 984.375

TC=368.75

Profit=TR-TC =  984.375 - 368.75 = 615.625

2:

A)

P=100-8Q

TR=P*Q=100Q-8Q²

MR=(TR)'=100-16Q

TC=50+80Q - 10Q² + 0.6Q³

MC=(TC)'=80-20Q+1.8Q²

MC=MR

100-16Q=80-20Q+1.8Q²

Q = 4.62475

P=63.002

TR=4.62475*63.002 = 291.369

TC=265.446

Profit=TR-TC=25.9223

B)

TR→MAX  => MR=0

MR=100-16Q

100-16Q=0

16Q=100

Q= 6.25

P=50

3:

Because in longer-run there will be entrance of competitors due to higher profits or/and market substitution by customers, and sometimes profits are lower than potential limit.

4:

A) + B) http://i306.photobucket.com/albums/nn270...

Q ...TC ....VC ....FC ...AVC ....ATC ....AFC ...MC(dq) MC(s)

1 ...64.2 ...14.2 ...50 ...14.2 ...64.20 ...50.00 ...12.6 ...14.2

2 ...75.6 ...25.6 ...50 ...12.8 ...37.80 ...25.00 ...10.4 ...11.4

3 ...85.4 ...35.4 ...50 ...11.8 ...28.47 ...16.67 .....9.4 ....9.8

4 ...94.8 ...44.8 ...50 ...11.2 ...23.70 ...12.50 .....9.6 ....9.4

5 ..105.0 ...55.0 ...50 ...11.0 ..21.00 ...10.00 ...11.0 ...10.2

6 ..117.2 ...67.2 ...50 ...11.2 ..19.53 ....8.33 ....13.6 ...12.2

7 ..132.6 ...82.6 ...50 ...11.8 ..18.94 ....7.14 ....17.4 ...15.4

8 ..152.4 ..102.4 ...50 ...12.8 ..19.05 ...6.25 .....22.4 ...19.8

9 ..177.8 ..127.8 ...50 ...14.2 ..19.76 ...5.56 .....28.6 ...25.4

10 .210.0 .160.0 ...50 ...16.0 ...21.00 ..5.00 .....36.0 ...32.2

MC(dq) means that marginal cost calculated using calculus method, but MC(s) means that marginal cost calculated using simple method MC(n)=TC(n)-TC(n-1).

C)

MC is decreasing at range 0≤Q≤4 and then increasing at range 4<Q≤∞

Yes, Grant's cost function illustrate all of these but on certain ranges.