You Have $64 to Spend on Fish (F) and Chips

question 21

Essay

You have $64 to spend on fish (F) and chips (C). Suppose the price per unit of fish (Pf) is $8 and the price of chips (Pc) is $2. Your utility function for fish and chips is given asC. How many units of C and F should you buy to exhaust all income and maximize utility?
First note that to maximize utility, you have to be at equilibrium. This means, the following condition has to be satisfied:
It is better to write this as:
Now substitute the corresponding entities in the above expression:
Cancelling the 2s in the denominator and cross-multiplying we get
C = 4 F
Now the second aspect of this is your income which is $64, which has to be spent on F and C. So your budget constraint should satisfy this condition:
64 = C Pc + F Pf or
64 = C 2 + 8 F and now from the previous condition we have
64 = (4 F) 2 + 8 F or
F = 4 units
C = 16 units and total utility is

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Definitions:

Quantifier

A symbol or phrase in logic that expresses the quantity of specimens to which a proposition applies.

Proposition's Form

The structure or pattern of a logical proposition, which determines its validity and can include elements like subject, predicate, and quantifiers in logic.

Nonstandard Quantifiers

Quantifiers that go beyond the traditional universal and existential quantifiers, often used in mathematical logic and linguistics to express quantities not easily defined by 'all' or 'some'.

Universal

In logic, pertaining to concepts that are general or applicable in all cases.