Question 2 | 25 Marks] a) The marginal utilities of two goods X and Y that Mary

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Question 2 | 25 Marks] a) The marginal utilities of two goods X and Y that Mary Phiri consumes and the required units uantity consumed) are given in the following table MUx (utils) Units MUy (utils 24 21 20 16 14 12 10 4 12 Where MUx and MUy are marginal utilities of good X and Y respectively. Let the price of good X and Y be K2 and K3 respectively and Mary has K24 to spend on two goods; i) Find the amount of the two goods that Mary should consume for her to maximize utility b) The demand and supply functions for a product (helicopter rides) are given by Demand function: Supply function: Q--5P 290 Q=10P-40 i) Calculate the equilibrium price and quantity algebraically ii) Plot the demand and supply functions in the form P=g(2)with clearly and well- iii) iv) v) vi) labelled diagrams Illustrate graphically the consumer and producer surplus at equilibrium.[1] Calculate both the consumer and producer surplus at equilibrium. Calculate the total surplus at equilibrium. If a tax of K15 per unit is imposed: find (i) (ii) The new supply function and plot it on the graph in (ii) The new equilibrium point (i.e. price and quantity) c) State and explain the three types of price discrimination.

Explanation / Answer

To find the optimal quantity which maximise May's utility , calculate marginal utility per dollar.

Px= $2 , Py= $3

And Income, I=$24

At Utility maximisation point , MUx/Px =Muy/Py

Mary spend all her money income on the consumption of goods x and y. We can see from the above table that MUx/Px = MUy/Py at many bundles like when Mary consumes 3 units of good x and 1 units of good y , Or When she consumes 4 units of good x and 2 units of good y , Or when she consumes 5 units of good x and 3 units of good y , Or when she consumes 6 units of good x and 4 units of good y.

But all her money get exhausted in the consumption of two goods x and y , when she consumes 6 units of good x and 4 units of good y.

Because then PxX + PxY = I

(2)(6)+3(4)=$24

Hence, the (6,4) i.e 6 units of good x and 4 units of good y is the bundle that Mary should consume for her to maximise utility.

Units MUx MUx/Px MUy MUy/Py 1 20 20/2=10 24 24/3=8 2 18 18/2=9 21 21/3=7 3 16 16/2=8 18 18/3=6 4 14 14/2=7 15 15/3=5 5 12 12/2=6 12 12/3=4 6 10 10/2=5 2 2/3=0.67

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