Question

A consumer gets 50 utils of utility from the consumption of the first unit of commodity- X. On the assumption that for every additional unit of X, he loses 10 utils of the utility, how many units of X will he consume if. It was available to him at Rs 5 per unit, and his marginal utility of money = 10?

Answer 1

Hint: Now we know that for equilibrium the condition is given by $\dfrac{M{{U}_{x}}}{{{P}_{x}}}=M{{U}_{m}}$ . Here we are given that the price per unit is Rs 5 and the marginal utility of money is 10. Hence we get the values of ${{P}_{x}}$ and $M{{U}_{m}}$ respectively. Hence we get the required values of $M{{U}_{x}}$. Now with each addition of unit he loses 10 utils of utility. Hence we can calculate the number of units by matching the value of $M{{U}_{x}}$ with the obtained value.

Complete step-by-step solution:
Now we are given a consumer gets 50 utils from the consumption of the first commodity. Now let the first commodity be ${{x}_{1}}$ hence the value of $M{{U}_{x}}=50$
Now he loses 10 utils of the utility with the addition of a unit of X.
Hence we can say $M{{U}_{x}}=40$ for ${{x}_{2}}$ , $M{{U}_{x}}=30$ for ${{x}_{3}}$ , $M{{U}_{x}}=20$ for ${{x}_{4}}$ , $M{{U}_{x}}=20$ for ${{x}_{5}}$ , $M{{U}_{x}}=10$ for ${{x}_{6}}$ , $M{{U}_{x}}=0$ for ${{x}_{7}}$ . where i in ${{x}_{i}}$ denotes number of units.
Now we also know that the price per unit is Rs 5.
Hence we get ${{P}_{x}}=5$.
Now we also know that his marginal utility of money is 10.
Hence, $M{{U}_{m}}=10$ .
Now we know that the condition form equilibrium is $\dfrac{M{{U}_{x}}}{{{P}_{x}}}=M{{U}_{m}}$
Hence now substituting the values we get $\dfrac{M{{U}_{x}}}{5}=10$
Now multiplying the whole equation by 5 we get $M{{U}_{x}}=50$.
Now we know that the value of $M{{U}_{m}}=50$ for ${{x}_{1}}$ .
Hence we get he has consumed just 1 unit.

Note: Marginal utility is widely used by economists to estimate how much of goods or services customers want to buy. Now if buying more than 1 item fails to bring the satisfaction then we call this case as 0 marginal utility. Hence here we have a case of zero marginal utility.