How to Calculate Mathematical Budget Constraint for Consumer
The mathematical budget constraint for a consumer with an income of $1600, who buys food for $10 each (f) and entertainment for $40 each (e), can be represented as follows:
Budget Constraint Equation:
10f + 40e = 1600
a. When the consumer buys 20 units of food:
10(20) + 40e = 1600
200 + 40e = 1600
40e = 1600 - 200
40e = 1400
e = 1400 / 40
e = 35
Therefore, when the consumer buys 20 units of food, they should buy 35 units of entertainment to satisfy their budget constraint.
b. Consumer keeps food consumption constant at 20 units:
10(20) + 100e = 1600
200 + 100e = 1600
100e = 1600 - 200
100e = 1400
e = 1400 / 100
e = 14
If the price of entertainment increases to $100 each, the consumer will buy 14 units of entertainment to satisfy their budget constraint.
Question: give the mathematical budget constraint for a consumer that has an income of $1600 and buys food for $10 each and entertainment for $40 each. a. When the consumer buys 20 units of food, how many units of entertainment should they buy? b. Suppose the consumer keeps their level of consumption of food constant at 20 units, and the price of entertainment increases to $100 each. How much entertainment will the consumer now buy? Budget constraint for a consumer: a. When the consumer buys 20 units of food, they should buy 35 units of entertainment. b. If the price of entertainment increases to $100 each, the consumer will buy 14 units of entertainment.