Using the model developed in The Economy Unit 3, Section 3.7, consider an individual who is facing a wage (w) of $20 per hour. Assume that their spending on goods and services cannot exceed their earnings per day. Maximum consumption (c) per day is: c = w(24 – t) where t = hours of free time per day. a) Initially when facing w = $20 per hour the individual chooses to work 10 hours per day and have 14 hours of free time per day. In a fully labelled diagram show the individual’s optimal combination of free time and consumption. (Fully labelled means that you must label both axes, correctly determine the vertical axis and horizontal axis intercepts, label the slope of the budget constraint and show the optimal amount of free time and consumption associated with it.) b) Assume that the wage increases to $30 per hour. Show the new utility maximizing combination of free time and consumption in your diagram from a). c) On your diagram decompose the overall change in hours of free time in response to the wage increase into the (i) income effect and (ii) substitution effect.
Using the model developed in The Economy Unit 3, Section 3.7, consider an individual who is facing a wage (w) of $20 per hour. Assume that their spending on goods and services cannot exceed their earnings per day. Maximum consumption (c) per day is: c = w(24 – t) where t = hours of free time per day. a) Initially when facing w = $20 per hour the individual chooses to work 10 hours per day and have 14 hours of free time per day. In a fully labelled diagram show the individual’s optimal combination of free time and consumption. (Fully labelled means that you must label both axes, correctly determine the vertical axis and horizontal axis intercepts, label the slope of the budget constraint and show the optimal amount of free time and consumption associated with it.) b) Assume that the wage increases to $30 per hour. Show the new utility maximizing combination of free time and consumption in your diagram from a). c) On your diagram decompose the overall change in hours of free time in response to the wage increase into the (i) income effect and (ii) substitution effect. d) On your diagram, illustrate and explain how the wage increase can lead them to have: i. more consumption and more free time ii. more consumption and less free time iii. less consumption and more free time
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