Question

You have $60 to spend on food. You are interested in the nutritional content of the food, but you cannot purchase carbs and proteins separately. You can buy steak and loaves of bread. You have the following price and nutrition information: Steak costs $6 a pound and one pound has 12 grams of protein and 6 grams of carbs. Loaves of bread cost $5 a pound and one pound has 5 grams of protein and 15 grams of carbs. (a) Derive the absolute price of a gram of protein (b) Derive the absolute price of a gram of carbs (c) At what rate can you exchange 1 gram of protein for 1 gram of carbs? Explain how you obtain this number and what determines it (d) If you spend all your money on loaves of bread, how many grams of carbs will you consume? How many grams of protein will you consume? (e) If you spend all your money on steak, how many grams of carbs will you consume? How many grams of protein will you consume? (f) Derive the equation of the individual's budget constraint (g) Draw the budget set. Make sure that you label all the relevant quantities

Answer 1

a) For absolute price of gram of protein and carbs , we use the equations given in the question

so $6 = 12x+6y

$5= 5x+15y

where x is the number of proteins in 1 gram and y is the number of carbs in 1 gram

equating them we get x= $2/5 per gram = $0.4 /gram

puuting it in any equation 1 or 2 we get

y=3/15= 1/5= $0.2/gram

so a) absolute price of a gram of protein is $0.4/gram

and b) absolute price of a gram of carbs is $0.2/gram

c) To find the exchnage rate we look at the ratio of exchange ie (price of protein /gram )/price of carb per gram

= (0.4/gram )/(0.2/gram ) = 2

cost of 1 gram of protein is $0.4/gram and 1 gram of carb is $0.2/gram

if we need to exchange 1 gram of protein with 1 gram of carb , the price paid for protein is twice the price for carbs. so for every 1 gram of protein , we need equivalently 2 garms of carbs and for 1 gram of carbs we need 1/2 grams of proteins.

d) if all money is spend on loave of bread , then it means that we can buy 12 loaves of bread ie 60/5(total income / price of 1 bread)

in 1 l;oave of bread we had5 grams of protein so in 12 loaves we have 12*5 = 60 grams of proteins

similarly in we have 15 grams in 1 loave of bread so carbs in 12 loaves would be 12*15= 180 grams of carbs

e) if we consume steak all of it with our whole income , we can consume 10 steaks

so carbs and proteins would be 10 times the amount

ie in 10 steaks we consume 120 grams of proteins and 60 grams of carbs.