Question

Create a conceptual demand function, cost function for a Tesla Product

How can Tesla maximize profit ?

Draw the functions

Answer 1

The Tesla products are more of luxury nature and thus the demand is highly elastic, implying that a price increase in the Tesla product will impact the quantity demanded in a big way. Thus the slope coefficient (b) of a typical demand function : P = a-bQ +cS has to be huge. Besides, the coefficient of c which is the coefficient for the close substitutes to the Tesla product is also high. Thus a small change in the price of its close substitutes or the other brands will impact the demand in a big way. Suppose: a = 10 , b = -2, c= 2.

The cost function of tesla product will be: C = k + wQ + zQ2: This imply that the cost function is concave such that k = 100, w = 10, z = 5

SO demand : P = 10 – 2Q + 2S

Cost: C = 100 +10Q + 5Q^2

For profit maximisation, tesla must keep prices less to increase profit by increasing quantity. This is ecause the tesla products are luxury goods with high price elasticity. The cost functions are increasing so it must reduce its costs (fixed cost and new technology that reduce the cost of additional production).

Plotting: suppsose S is fixed at say 10 units:

S= 10
Q	Price	Cost	Profit
0	180	100	-100
1	175	115	60
2	170	140	200
3	165	175	320
4	160	220	420
5	155	275	500