Question

1 unit increase in price in a market decreases the demand amount by 1 unit and increases supply amount by 3 units. The autonomous demand is 48 units. While the price is zero, the average supply is -4 units.
a) Calculate the values of the balance points.
b) In this market, 2 unit tax has been applied for each unit of the firm sold. Calculate the values of new balance points after tax.

Answer 1

Ans. For demand function,

As 1 unit increase in price decreases demand by 1 unit, thus, the slope of the demand curve which represents change in demand due to change in price is -1. Also, the autonomous demand is 48 units, so, demand function is,

Qd = -P + 48

Similarly, tge supply function has a slope of 3 and as supply equals -4 units when price is zero, so, supply function is,

Qs = 1/3 * P -4

a) When market is balanced,

Supply = Demand

=>1/ 3 * P - 4 = -P + 48

=> P = 39 units and from the demand and supply functions,

Qd = Qs = 9 units

b) Suppose a 2 unit tax is imposed which increases the price for consumers by t units and decreases the price recieved by the sellers by (2-t) units.

=> New demand function, Qd = -(P + t) + 48

And

New supply function, Qs = 1/3 (P - (2-t)) - 4

At balance point,

Qd = Qs

=> -(P + t) + 48 = 1/3 (P+t - 2) - 4

=> 4/3 (P + t) = 158/3

=> P + t = 39.5 and we know P = 39 units
=> t = 0. 5 units

=> Qd = 8.5 units

And Qs = 8.5 units

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