Consumer demand.

Question

a) Consider the following consumer demand function for Unga.

X_{u= 10 + M/10P}

Where

_{M= Kshs 1,500, consumer income.}

_{P= Kshs30, price of Unga per Kilo.}

_{Required to:}

_{a) Find the consumer's demand for Unga.}

_{b) Find the consumer's demand with a new price of Unga @Kshs 20 per Kilo.}

_{c) compute the total change in demand due to the change in price from Kshs30 to Kshs20.}

_{d) Calculate the change in income necessary to make the original consumption of Unga just affordable when the prices of Unga is Kshs20 per Kilo.}

_{e) Find the level of income necessary to keep the consumer's purchasing power constant.}

Answer 1

a) To find the consumer's demand for Unga, we substitute the given values of M and P into the demand function: Xu = 10 + M/10P Xu = 10 + (1500)/(10*30) Xu = 10 + 5 Xu = 15

Therefore, the consumer's demand for Unga is 15 kilos.

b) To find the consumer's demand with a new price of Unga at Kshs 20 per kilo, we substitute the new value of P into the demand function: Xu = 10 + M/10P Xu = 10 + (1500)/(10*20) Xu = 10 + 7.5 Xu = 17.5

Therefore, the consumer's demand for Unga with a new price of Kshs 20 per kilo is 17.5 kilos.

c) To compute the total change in demand due to the change in price from Kshs 30 to Kshs 20, we subtract the new demand from the original demand: Change in demand = Original demand - New demand Change in demand = 15 - 17.5 Change in demand = -2.5

Therefore, the total change in demand due to the change in price is a decrease of 2.5 kilos.

d) To calculate the change in income necessary to make the original consumption of Unga just affordable when the price of Unga is Kshs 20 per kilo, we can rearrange the demand function to solve for M: Xu = 10 + M/10P Xu(10P) = 10P + M M = Xu(10P) - 10P M = 15(10*20) - 10