Mikaela drinks 10 sodas and 4 smoothies. Yesterday smoothies were $5 each and so
ID: 1116894 • Letter: M
Question
Mikaela drinks 10 sodas and 4 smoothies. Yesterday smoothies were $5 each and sodas were $2 each. Today things are different: The government has implemented a tax on sodas and their price has doubled to S4. The government has also revised the income tax so that Mikaela's income has increased. She can now afford to buy her usual 10 sodas and 4 smoothies per week. Part A What is Mikaela's income today? Part B Suppose smoothies are measured on the y-axis and sodas are measured on the x-axis. What is the absolute value of the slope of Mikaela's budget constraint today? L Part C Suppose Mikaela has discovered a new love for coffee and tea and would like to add both to her weekly beverage consumption. Coffee costs $2/cup and tea costs S1.50/cup. Mikaela would like to maximize utility given her income. If the marginal utility from consuming sodas is 8 and the marginal utility fromconsuming smoothies is 10, Mikaela should consumecups of coffee and cups of tea. Total utility: Coffee otal utility: Tea 40 60 70 74 74 50 80 95 100 103Explanation / Answer
Mikaela faces the following budget constraint yesterday and today
10 x PSodas + 4 x PSmoothies = Income.................... 10*2 + 4*5 = $40.............(yesterday)
10 x PSodas + 4 x PSmoothies = Income.................... 10*4 + 4*5 = $60.............(today)
Her income today is $60
Slope of budget constraint today = PSodas/PSmoothies = 4/5 = 0.8
Now with given total utilities, we find that MU/$ of coffee is 20, 10, 5, 2, 0 and MU/$ of tea is 50/1.5, 20, 10, 5/1.5, 2
We find that MUSodas/PSodas = 8/4 = 2 and MUSmoothies/PSmoothies = 10/5 = 2 we must find MU/$ of coffee and MU/$ of tea which is also 2. It turns out that coffee consumption is 4 units and tea is 5 units.