Susan obtains utility by consuming carrots C and enjoying leisure L. Suppose that she has a daily non-wage income Y of £100 and is paid a fixed hourly wage rate of £10 for every hour she works in a local coffee shop. Assume that Susan is a utility maximiser and is free to choose x hours of work per day where 0 ≤ x ≤ 10. Assume also that the unit price of C is £1. a) Suppose that L is measured on the horizontal axis and C on the vertical axis. Use these axes to draw the set of all C and L combinations that Susan can choose from. Write down Susan’s budget equation. b) Suppose that Su
Susan obtains utility by consuming carrots C and enjoying leisure L. Suppose that she has a daily non-wage income Y of £100 and is paid a fixed hourly wage rate of £10 for every hour she works in a local coffee shop. Assume that Susan is a utility maximiser and is free to choose x hours of work per day where 0 ≤ x ≤ 10. Assume also that the unit price of C is £1.
a) Suppose that L is measured on the horizontal axis and C on the vertical axis. Use these axes to draw the set of all C and L combinations that Susan can choose from. Write down Susan’s budget equation.
b) Suppose that Susan’s preferences over carrots and leisure are expressed by the following utility function: U(C,L) = min{C, 10L}. Calculate Susan’s optimal consumption bundle, both algebraically and graphically. Calculate the value of MRS at the optimal choice.
c) Suppose instead that Susan’s preferences are such that indifference
d) Following on with the assumptions from c), suppose that the employer offers Susan a higher overtime wage rate £15 for the amount of work she does in excess of 5 hours. By considering her marginal rate of substitution (MRS) of L for C, show that Susan will work some overtime hours. Your explanation should give a detailed analysis of the effects of the introduction of the overtime wage rate on Susan’s choice and illustrate them with properly drawn diagram(s).
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