# Economics

Economics

Q1. Sometimes firms conduct experiments where they temporarily change prices (this may be done with selective coupons and other discounting methods) to see how the consumer responds to a price change. Let’s assume that our firm charges \$10 per unit of output and on average has 600 units sold per day. However, for the last week the firm offered a \$1 discount and charged only \$9 per unit of output. During the week of the discount the firm observed that the average daily sales were 700 units.

(i) If we operate under the assumption of ceteris paribus, what is the best linear representation of the demand faced by the firm [please provide the equation for the demand in terms of Q = a+bP].

• Price (OLD)                         =             \$ 15

Price (NEW)                        =             \$ 10

Qty Demand(OLD)           =             400

Qty Demand(NEW)         =             1000

Calculating the Percentage Change in Quantity Demanded

[QDemand(NEW) – QDemand(OLD)] / QDemand(OLD)

[1000 – 400] /400 = (600/400) = 1.50

In percentage terms this would be 150.00 %

Calculating the Percentage Change in Price

[Price(NEW) – Price(OLD)] / Price(OLD)

[10 – 15] /15 = (-5/15) = – 0.3333

In percentage terms this would be -33.33 %

Price Elasticity of Demand            = (% Change in Quantity Demanded)/(% Change in Price)

=             1.50/-0.333

=             -4.50045

We will take absolute value and ignore the negative sign. Hence price elasticity of demand when the price of goods decrease from \$ 15 to \$ 10 is 4.50045.

Since Price elasticity of demand is greater than 1, Goods/Service is sensitive to price and Demand is price elastic.

• We have:

Price (OLD)                         =             \$ 15

Price (NEW)                        =             \$ 10

Qty Demand(OLD)           =             400

Qty Demand(NEW)         =             1000

Calculating the Percentage Change in Quantity Demanded

[QDemand(NEW) – QDemand(OLD)] / QDemand(OLD)

[1000 – 400] /400 = (600/400) = 1.50

In percentage terms this would be 150.00 %

Calculating the Percentage Change in Price

[Price(NEW) – Price(OLD)] / Price(OLD)

[10 – 15] /15 = (-5/15) = – 0.3333

In percentage terms this would be -33.33 %

Price Elasticity of Demand            = (% Change in Quantity Demanded)/(% Change in Price)

=             1.50/-0.333

=             -4.50045

We will take absolute value and ignore the negative sign. Hence price elasticity of demand when the price of goods decrease from \$ 15 to \$ 10 is 4.50045.

Since Price elasticity of demand is greater than 1, Goods/Service is sensitive to price and Demand is price elastic.

• The firm charges \$10 per unit of output and on average has 600 units sold per day.

When it offered a \$1 discount and charged only \$9 per unit of output, its average daily sales were 700 units.

Now these can be used to construct the demand function.

Take the following form of the demand function => P = a – bQ, here b is the slope of the demand function.

Now two equations result from the above information

10 = a – 600b,

9 = a – 700b

Solve them for a and b as:

10 – 9 = a – 600b – a + 700b

1 = 100b

b = 0.01

a = 16

Hence the demand function is P = 16 – 0.01Q or Q = 1600 – 100P

This is the best linear representation of the demand faced by the firm.

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