Tutorial 5 (MicroEconomics) px/PY

Tutorial 5 (MicroEconomics)
P_X/P_Y = MU_X/MU_Y









Practice questions.

1. 
   Martha’s current marginal utility from consuming orange juice is 100 utils per ounce and her marginal utility from consuming coffee is 50 utils per ounce.
   
   1. 
      What is the marginal rate of substitution of orange juice in terms of coffee?
      
   2. 
      If orange juice costs 25 cents per ounce and coffee costs 20 cents per ounce, which one should Martha buy first to maximize her total utility? Explain why.
      
   3. 
      What should be the price of coffee for Martha to be indifferent between orange juice and coffee?
      
   4. 
      If the income of the Martha is $10 construct budget line.
      

2. 
   Suppose a consumer’s income is M=$1,200 per month, all of which he spends on some combination of rent and restaurant meals. If restaurant meals cost $12 each and if the monthly rent for an apartment is $3 per square foot, draw this consumer’s budget constraint with his monthly quantities of restaurant meals per month on the vertical axis and apartment size on the horizontal axis. Is the bundle (300 square feet/month, 50 meals/month ) affordable?
   

3. 
   The utility of John is represented by U(x,y)=x*y. This implies, if he consumes 4 units of x and 5 units of y, then his utility (degree of satisfaction) is 4*5=20.
   

1. 
   Find at least 5 choices which give him the utility of 100, and draw the indifference curve.
   
2. 
   If the price of x good is $1 and the price of y good is $5 which option gives him minimum cost.
   
3. 
   If he has the budget of $50 what is the maximum utility he can reach? What is the optimum bundle of two goods?
   
4. 
   Keeping budget the same what is the optimum bundle and maximum utility if the price of good x increases to $2.
   
5. 
   Keeping budget the same what is the optimum bundle and maximum utility if the price of good x increases to $5.
   
6. 
   Derive the demand curve for x good at different price levels.
   

4. 
   Daniel says that 1 unit of good x is always as good as 4 units of good y.
   
   1. 
      Write down an example of Daniel’s utility function. What kind of goods are these for him?
      
   2. 
      For prices p_x = 4, p_y = 2, and income I = 60. Find the optimal bundle (x₀, y₀) and show it on the graph?
      
   3. 
      Suppose that the price of x increases to p_x = 7. Find the substitution, income, and total effects of the price change on the consumption of x and y.
      
   4. 
      For the price p1y = 2 and income of I = 60, derive Daniel’s demand function for good x.