Answer to Question #278389 in Microeconomics for Kasper Wiehl

Question

Hi

Can somebody help with me with the below? 

Thanks in advance

Information:

Q = 33.33 - 0.000004167 * P + 0.04167 * PCO2 - 0.4167 * r - 0.00833 * Pel, where

Q is the quantity sold, P is the price, PCO2 is the price of the EU's CO2 quotas, measured in euros per tonnes, cf. Chart 1, r is the banks' average lending rate measured in per cent. pa., and Pel is the Nordpool wholesale price of electricity excl. network and system tariffs as well as charges, measured as Danish kroner per MWh (mega-watt-time).

P can here be set to DKK 4,000,000, PCO2 can be set to 62, r to 2.37 and Pel can be set to 250.

Question:

Calculate the price elasticity as well the cross-price elasticities with regard to as well The CO2 price, the interest rate and the electricity price. Then discuss whether the signs on the price elasticities can be justified.

Answer 1

$Price elasticity=\frac{dQ}{dP}\times\frac{P}{Q}$

$=- 0.000004167\times\frac{4,000,000}{33.33 - 0.000004167(4,000,000) + 0.04167 (62) - 0.4167(2.37) - 0.00833(250)}= -1.03$

$Cross -Price elasticity with regard to CO2=\frac{dQ}{dPCO2}\times\frac{PCO2}{Q}$

$=0.04167\times\frac{62}{33.33 - 0.000004167(4,000,000) + 0.04167 (62) - 0.4167(2.37) - 0.00833(250)}= 0.159$

$Cross -Price elasticity with regard to r=\frac{dQ}{dr}\times\frac{r}{Q}$

$=-0.4167\times\frac{2.37}{33.33 - 0.000004167(4,000,000) + 0.04167 (62) - 0.4167(2.37) - 0.00833(250)}= -0.061$

$Cross -Price elasticity with regard to Pel=\frac{dQ}{dPel}\times\frac{Pel}{Q}$

$=-0.00833\times\frac{250}{33.33 - 0.000004167(4,000,000) + 0.04167 (62) - 0.4167(2.37) - 0.00833(250)}= -0.128$

The signs on the price elasticities can be justified by the relationship between the quantity sold and and the price. If a decline in price leads to an increase in quantity sold, then the price elasticity will be a negative. When an increase in price causes an increase in quantity sold, the price elasticity will be positive. However, price elasticity and cross price elasticity measures the absolute change in quantity resulting from change in price. As a result, the elasticity values are read in absolute values.