Q1. A consumer consumes two commodities, 1 and 2 . A consumption bundle is represented by a vector which lists the quantities of the commodities 1 and 2, respectively. The following consumption bundles are on the consumer's budget plane, (2,6) and (5,2). (a) Write the equation of the budget line in the form x(t)=x0+tv, where x0 is a point on the budget line and v is the direction of the line. (b) Let the consumer's utility function be given by U(x1,x2)=x1x2. Calculate the derivative of this function at (2,6) in the direction (3,4). In calculating this derivative use the unit direction vector, that is, a direction vector of length 1. (c) Do the same as in (b) but this time in the direction (3,4). (d) Using (a), (b) and (c) determine whether the consumer is maximizing utility at (2,6), if not, which commodity will the consumer consume more of and which commodity will the consumer consume less of to increase utility, but still satisfy the budget line